Question

Find the value to three places of decimals √2+1/√5
It is given that √10 = 3.162 and √5 = 2.236​

Answer 1

Answer:

1.076

$multiply \: and \: divide \: by \: \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1}. \\ \\ \implies{\frac{ \sqrt{2} + 1 }{ \sqrt{5} } \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1}} \\ \\ \implies{\frac{ {(\sqrt{2})}^{2} - {1}^{2} }{ \sqrt{5 \times 2} - \sqrt{5} }} \\ \\ \implies{\frac{2 - 1 }{ \sqrt{10} - \sqrt{5} }} \\ \\\implies{\frac{1}{ \sqrt{10} - \sqrt{5} }} \\ \\ putting \: given \: decimals \: in \: this \: fraction.then \\ \\ \implies{ \frac{1}{3.165 - 2.236} = \boxed{\frac{1}{0.929} = 1.076 \: .}}$

Answer 2

Solution -

We have,

• $\sf{\dfrac{\sqrt{2} + 1}{\sqrt{5}}}$

⠀

Firstly, we have to rationalise the denominator

$\tt\dashrightarrow{\dfrac{\sqrt{2} + 1}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}}$

⠀

$\tt\dashrightarrow{\dfrac{(\sqrt{2} + 1) \sqrt{5}}{\sqrt{5} \times \sqrt{5}}}$

⠀

$\tt\dashrightarrow{\dfrac{\sqrt{10} + \sqrt{5}}{5}}$

⠀

From the given values, i.e.,

• $\sf{\sqrt{10} = 3.162}$
• $\sf{\sqrt{5} = 2.236}$

⠀

Putting the values

$\tt\dashrightarrow{\dfrac{3.162 + 2.236}{5}}$

⠀

$\tt\dashrightarrow{\dfrac{5.398}{5}}$

⠀

$\bf\dashrightarrow{1.079}$

⠀

Hence,

• The required value is 1.079.

━━━━━━━━━━━━━━━━━━━━━━